Molecular Vibrations

Pedagogical classic and essential reference focuses on mathematics of detailed vibrational analyses of polyatomic molecules, advancing from application of wave mechanics to potential functions and methods of solving secular determinant.

This volume focuses on molecular clusters, bound by van der Waals interactions and hydrogen bonds. Twelve chapters review a wide range of recent theoretical and experimental advances in the areas of cluster vibrations, spectroscopy, and reaction dynamics. The authors are leading experts, who have made significant contributions to these topics. The first chapter describes exciting results and new insights in the solvent effects on the short-time photo fragmentation dynamics of small molecules, obtained by combining heteroclusters with femtosecond laser excitation. The second is on theoretical work on effects of single solvent (argon) atom on the photodissociation dynamics of the solute H2O molecule. The next two chapters cover experimental and theoretical aspects of the energetics and vibrations of small clusters. Chapter 5 describes diffusion quantum Monte Carlo calculations and non additive three-body potential terms in molecular clusters. The next six chapters deal with hydrogen-bonded clusters, reflecting the ubiquity and importance of hydrogen-bonded networks. The final chapter provides the microscopic theory of the dynamics and spectroscopy of doped helium cluster, highly quantum systems whose unusual properties have been studied extensively in the past couple of years.

Nonlinearity and Chaos in Molecular Vibrations deals systematically with a Lie algebraic approach to the study of nonlinear properties of molecular highly excited vibrations. The fundamental concepts of nonlinear dynamics such as chaos, fractals, quasiperiodicity, resonance, and the Lyapunov exponent, and their roles in the study of molecular vibrations are presented.The 20 chapters cover the basic ideas, the concept of dynamical groups, the integrable two-mode SU(2) system, the unintegrable three-mode SU(3) system, the noncompact su(1,1) algebraic application, su(3) symmetry breaking and its application and the quantal effect of asymmetric molecular rotation. Emphasis is given to: resonance and chaos, the fractal structure of eigencoefficients, the C-H bend motion of acetylene, regular and chaotic motion of DCN, the existence of approximately conserved quantum numbers, one-electronic motion in multi-sites, the Lyapunov exponent, actions of periodic trajectories and quantization, the H function and its application in vibrational relaxation as well as the Dixon dip and its destruction and chaos in the transitional states. This approach bridges the gap between molecular vibrational spectroscopy and nonlinear dynamics.The book presents a framework of information that readers can use to build their knowledge, and is therefore highly recommended for all those working in or studying molecular physics, molecular spectroscopy, chemical physics and theoretical physics. * Discusses nonlinearity and chaotic phenomena in molecular vibrations* Approaches the complicated highly excited molecular vibration* Provides clear information for students and researchers looking to expand knowledge in this field

This book presents a comprehensive theoretical basis of symmetry representations of molecular vibrations, matrix representation of symmetries, and the elements of group theory that are relevant to other symmetry elements/operations, crystallographic and molecular point groups. The book helps understand the reducible and irreducible representations of symmetry matrices and then derive the normal modes of vibration of different molecules by using suitable techniques independently. Targeted to graduate students and researchers, this book aims not only to derive the normal modes of vibration of any given molecule themselves but also compares and verifies them with the experimentally found modes by using IR and Raman-related techniques. For the first time in the crystallographic history, this book presents the group multiplication tables of all 32 point groups in both international and Schoenflies notations.

This book focuses on the main idea that highly-excited molecular vibration is a nonlinear, many-body and semiclassical system. Therefore, many ideas and techniques in nonlinear fields such as chaos, resonance, Lyapunov exponent, etc. can be incorporated into this study. Together with the Lie algebraic coset algorithm, readers are able to approach the topics in a simple arithmetic and realistic way in contrast to the traditional solving of Schrödinger equation. Covering the author's research in over two decades, these works bridge the gaps between molecular vibration and nonlinear sciences, many new characters are introduced for molecular highly-excited vibration from a fresh viewpoint of nonlinearity, especially, the chaos. Related works of the elementary ideas in this field can be found in the first three chapters for the readers to be familiar with, while the rest of the chapters offer concrete examples with flourishing ideas and results on system dynamics which are not known or neglected by the traditional wave function algorithm.